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I was surprised to see that, in Germany, where they receive a fewer amount of energy with respect to other countries, by the end of 2003 had clearly invested more in solar panels than many other countries which get more solar energy than them.

Solar Energy Potential At Different Latitudes

I was surprised
to see that, in Germany, where they receive a fewer amount of energy with
respect to other countries, by the end of 2003 had clearly invested more
in solar panels than many other countries which get more solar energy than
them.

by Gerardo
R. Ayala González, Productos A-Chá

Introduction

The content of this article was originally articulated
from some notes and graphs I began using in my efforts to explain persons
about the real expectations they can have regarding investments in solar
water heating devices. The first time I used this material publicly
was at a conference in a CAINTRA business exposition in Cintermex, in
Monterrey. My community, where I am focusing now for this new born business,
has an almost complete blindness regarding solar energy today. Generally,
people do not think about it and do not consider it a real opportunity
for saving money. Very few people take solar energy as a serious subject;
I sometimes feel like &quot;preaching in the middle of the desert".

I put together these ideas for the first time, in order
to raise the possibility of potential customers to get some curiosity
and interest about solar energy.

People's interest in solar energy

I have offered my products to persons whose job is related
to energy saving and / or ecology, and who think it is good for all
human beings, but guess what… most have never thought about installing
a solar water heater in their homes; nor any other renewable energy
type of device. Since there has been null or little offer of this type
of devices, most have never known of any company who sells them. Most
people do not know solar water heating is here for mankind; when they
hear about it, they immediately relate the conversation to photovoltaic
energy; and ask if they can save electricity on their conventional air
conditioning appliances. Only swimming pool vendors are offering some
type of solar energy with very little success.

After one year since I began this adventure in the solar
energy environment, I've been learning and observing many interesting
aspects of people behavior, that I did not expect. The most interesting
aspect I have observed in presales activities is that there is a clear
trend of the type of profile of persons who are open to talking about
the possibility of acquiring solar energy devices: Either they a) understand
about &quot;energy" and their work or hobbies are related to it, or they
are b) persons of an age at which they start worrying about their living
income in the future. It is difficult for me to open conversations about
it in businesses, unless I speak with the owner.

Focus of this article

And so, I began looking for ways to explain why SWH
is economically convenient, and why in our community, Monterrey, located
at the north-east of México, about a hundred miles from the Texan border,
solar energy is a real a gift from nature. To be more specific, at the
latitude where we are located, we receive almost the most energy that
any community can receive in the globe. We get almost as much solar
energy as they receive at the Equator; 98%.

I want to share with you, Earth Toys e-magazine readers,
in a very pragmatic manner, a set of basic physical concepts, that explain
why the amount of solar energy varies at the different points in the
globe. There are some other factors that I will not mention here, because
my mission with this writing is focused to beginners. But there are
more factors.

Variables that affect the amount of solar energy delivered
at each part of the globe

There are two main variables that affect the
amount of solar energy delivered at every part of the world: a) Sun
rays inclination at the specific geographical point; and b) Thickness
of the atmosphere between the specific point and the sun.

Figure 1 shows that at a specific point in the globe,
there can be two extreme thicknesses of atmosphere between the sun and
the point on the earths surface; in one day. At any place between the
two tropics, there are moments where the sun can be at an angle of 90°
at noon (right over our heads), and also at an angle of 0° at sunset.
In places off the mentioned earth's piece of surface, we never have
it at 90°, but we do have a maximum angle, depending on the respective
latitude. When the sun is at the maximum angle, the energy delivered
is highest. This is because the thickness of the atmosphere is or tends
to be d 1 (Figure 1). As you must have experienced, at this time it
is dangerous for your eyes to look directly to the sun; and you should
protect your skin against its rays.

On the other hand, when the sun is at its minimum angle,
the energy delivered is least. As an example, imagine when you are in
the beach or any other place without mountains around. When you see
the sun very low, you are able to stare at it without your eyes being
hurt by its rays. You can even take pictures of it with any regular
amateur camera. That is because, between you and the sun, the layer
of atmosphere is very thick, and it filters most of its light. See Figure
1.

As the sun moves from a high position to a lower one,
little by little, the energy you are receiving, diminishes until it
hides under the horizon.

In Figure 2, you can observe that the rotation axis
of the earth, is not perpendicular to the earth's translation plane
around the sun. There is an inclination of a 23.5 ° angle. The tropics
are two parallel lines around the earth one at the north and the other
at the south of the equator. These lines are respectively the ones where
the sun gets at 90° with respect to the earth's surface, when it reaches
its highest angle in the solstices. The June 21st solstice is the moment
when the sun gets its highest angle at noon in the north hemisphere;
and its lowest angle in the southern one. And it is exactly perpendicular
to the Tropic of Capricorn.

Every December the 21st, the same phenomenon happens
but on the other Tropic. The sun is, at noon, exactly over the Tropic
of Cancer . At that time, it is the beginning of summer in the southern
hemisphere, and the beginning of winter in the northern one.

In order to observe the whole yearly cycle, take a look
at Figure 3. Notice how the sun rays vary their inclination on the surface
of the earth, at the different points of it's yearly rotation cycle.

Solar energy delivered per square meter on the earth

Now lets get back to earth. See Figure 4 and think about
a piece of concrete sidewalk on the ground. Suppose you cut the sidewalk
in a square, one meter by one meter piece; upper part of the Figure.
Then think about the same piece of the sidewalk being observed laterally;
so that you can only see its thickness and a one meter wide.

In Figure 5, observe the same piece of concrete sidewalk.
If the sun is at an angle of 90° exactly at noon, you can imagine a
one meter wide band width of sun rays hitting on the one square meter
piece of sidewalk. As mentioned above, this is the most solar energy
amount, that the piece of sidewalk can receive.

In Figure 6 we see that if the sun angle inclines by
45°; the same band width of solar rays cannot all hit on the same piece
of sidewalk. Some of the rays, by geometrical reasons, hit outside of
it. This portion that hits outside is the proportional part of energy
that will not be delivered on that square meter of piece of sidewalk.
Observe that from the ten equal spaces of the band width of solar rays,
about two and a half of them, hit out of the same one square meter piece
of sidewalk. It means, that at this position of the sun over the same
point in the earths surface, only about 75% of the radiation is being
delivered. Just because of the inclination of the sun.

The same thing happens to the whole world. See Figure
7. At the equator, the sun hits, at some point of the day, exactly at
a 90° angle, all year long. That is why they receive the highest level
of solar energy.

But, the same does not happen on the whole northern
hemisphere. As you move from the equator to the north, the angle of
the sun declines. And in the same proportion of this inclination,
the corresponding geographical point receives less and less solar rays,
and thus, solar energy. And as mentioned above, see in Figure 1
that not only the sun's angle affects the energy delivered. As you move
to the north, the thickness of atmosphere is bigger between the sun
and the earths surface. The thickness grows geometrically as you move
further north.

Gathering the most possible solar energy

Figure 8 shows three graphs that represent the average
monthly solar energy delivered in Monterrey, México, in Kilo-Watt-Hour
per square meter. Monterrey is at about latitude 25.6. The picture shows
the monthly average amount of energy delivered every month in a year,
in solar panels at different angles.

Observe what happens if the surface is at 0° with respect
to the earth surface (blue line). See how in summer time, when the sun
is almost at 90° we get the highest amount of energy. But in winter,
at the far left and right of the graph, we get the least, because the
sun inclines, as explained above.

On the other hand, if the surface has an inclination
of 90° against the earth surface, and it is summer time, the energy
delivered in the same plane, is very little. It is because the sun rays
tend to hit the plane at a very inclined angle. In winter we get a little
more, because the sun lowers and hits the plane in a less inclined angle.
The 45° graph, shows its respective behavior.

Since the sun varies its angle during the day and during
the year, there is an angle for every point in the world, that optimizes
the delivered radiation to be captured in the plane of a solar panel.
There are different manners to calculate it, and there are also some
simple rules to do it; always related to the latitude and longitude
of the geographical point in the globe. In Figure 9 you'll see that the further you
go to the north, from the equator, the higher the angle of your solar
panel you need in order to optimize energy absorption.

Figure 10 shows the amount of solar energy that is delivered
in different parts of the world. For space reason I did not add more
examples, but in order to have an idea of some other locations, see
Fig. 7.

When I found on the Internet a Spanish report about solar
energy, I was surprised to see that, in Germany, where they receive
a smaller amount of energy with respect to other countries, by the end
of 2003, they had clearly invested more in solar panels than many other countries
which get more solar energy than them. By the end of 2002, México had
installed about .5 millions of square meters of solar panels, while
Germany, by 2003 had installed 5.5 million of square meters. I also
read a Spanish report that showed an example of an apartment building
where 38 square meters of solar panels were installed with an expected ROI of 5% in Madrid. I made calculations for the same type of building
facility using the same parameters, supposing the same building in Monterrey,
and to my surprise I learned that the same project in Monterrey, would
be having a ROI of 35.3 %; with an important reduction in the amount
investment.

I hope this article can be of help to those who are
or will be deciding on a project to install solar water heating systems.
It has been my intention to provoke curiosity in people, about the benefits
everyone can have on their own. I made an effort to do some mathematics,
and investigating different sources in order to put these ideas together
just as a intent to provoke in them a disquietude for the benefit of
our common home: The Earth.

Acknowledgements

Thanks to: Sara, Magda and Gerardo Noé Ayala, respectively
my daughter, son and wife, for their support in the investigation and
drawing of the ideas that were needed to put together this article.